Reconst nstruct ruct Radio o Map with Automatic atically ally - - PowerPoint PPT Presentation

Reconst nstruct ruct Radio

• Map with Automatic

atically ally Constru tructed cted Gaussia sian n Proces ess s for Localiz lizatio ation

目 录

C O N T E N T

01 | Background 02 | Gaussian Process 03 | Kernel Selection 04 | Model Ensemble 05 | Experiment

Page . Page . 3

1

P A R T O N E

Background

GPS： time consuming Power consuming Turn on meter Base station Signal strength

• indoor localization use

fingerprinting

• creating a radio map
• Received Signal Strength

Indicators (RSSI) values

• btained from multiple

access points (APs)

• a large outdoor

environment

• sample thousands of

survey sites to construct a fine grain radio map

• a university usually

needs hundred thousand training data

SJTU 3G 4G Yindu Road 3G 4G About one million sample data 20 square kilometers

2

P A R T T W O

Gaussian Process

Given a training set 𝐸 = 𝒚𝑗, 𝑧𝑗 𝑗 = 1, … , 𝑜} How to calculate the output 𝑧∗ for a new input 𝑦∗ Linear regression? – Least Square Method Nonlinear regression?

• - Gaussian Process

Rela elation

• nship

ip to Lin inear ar Regr egression

• n
• In logistic regression, the input to the sigmoid

function is where are parameters.

• A Gaussian process places a prior on the space of

functions f directly, without parameterizing f.

• Therefore, Gaussian processes are non-parametric
• more general than standard regression the form

not limited by a parametric form

T

f x b   



Assume 𝒛 = {𝑧1, 𝑧2, … , 𝑧𝑜} obey multivariate Gaussian Distribution 𝑧1 ⋮ 𝑧𝑜 ~𝑂 0, 𝐿 → 𝒛~𝑂 0, 𝐿 Where Given a training set 𝐸 = 𝒚𝑗, 𝑧𝑗 𝑗 = 1, … , 𝑜} How to calculate the output 𝑧∗(RSS) for a new input 𝑦∗（longitude/latitude）

• A Gaussian process any finite number of which have

joint Gaussian distributions.

• A Gaussian process is fully specified by its mean

function m(x) and covariance function k(x,x’).

• Two things to define our GP:
• choose a form for the mean function.
• choose a form for the covariance function

De Definiti nition n of GP GP

( , ) f gp m k

For new input data y* joint distribution defined as:

Get conditional distribution： Mean and variance:

Maxlimum: Hyper-parameters:：

Tun une Hyper-Par aram ameters

Maxlimum the log likelihood: (conjugate gradients)

SE kernel：

Hype per-parameters

𝜏

𝑔 2：overall vertical scale of variation of the latent value.

𝑚： characteristic length-scale

• short means the error bars can grow rapidly away from the

data points.

• large implies irrelevant features .

𝜏𝑜

2: noise variance

The covariance function defines how smoothly the (latent) function f varies from a given x.

Hype per-parameters

Different hyper parameters Bias & Variance trade off

left with small 𝑚 right with large 𝑚

3

P A R T t h r e e

Kernel Selection

Squared Exponential Kernel Periodic Kernel Linear Kernel

（1）ka + kb = ka(x, x′) + kb(x, x′) （Summation） （2）ka × kb = ka(x, x′) × kb(x, x′) （Multiplication）

Automatic Mo Model Construction

choosing the structural form of the kernel: a black art

• Search over sums and

products of kernels

• Maximizing the BIC(M)
• Show how any model be

decomposed into different parts BIC trades off model fit and complexity

4

P A R T F O U R

Model Ensemble

1)average out biases 2)reduce the variance 3)unlikely to overfit

Don’t Overfit! Averaging multiple different green lines should bring us closer to the black line.

Linear regression SVR Gradient Tree Boosting Xgboost GP (RQ) GP (Compose) Rate Averaging Blending

5

P A R T F I V E

Experiment Results

6

P A R T S I X

Q&A